Mechanics of Composite Elasmoid Fish Scale Assemblies and Their

journal of the mechanical behavior of biomedical materials 19 (2013) 75–86

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Mechanics of composite elasmoid ﬁsh scale assemblies and their bioinspired analogues

Ashley Browninga, Christine Ortizb,n, Mary C. Boycea,n aDepartment of Mechanical Engineering, 77 Massachusetts Ave, Massachusetts Institute of Technology, Cambridge, MA, USA bDepartment of Materials Science and Engineering, 77 Massachusetts Ave, Massachusetts Institute of Technology, Cambridge, MA, USA article info abstract

Article history: Inspired by the overlapping scales found on teleost fish, a new composite architecture Received 28 July 2012 explores the mechanics of materials to accommodate both flexibility and protection. These Received in revised form biological structures consist of overlapping mineralized plates embedded in a compliant 5 November 2012 tissue to form a natural flexible armor which protects underlying soft tissue and vital Accepted 11 November 2012 organs. Here, the functional performance of such armors is investigated, in which the Available online 24 November 2012 composition, spatial arrangement, and morphometry of the scales provide locally tailored Keywords: functionality. Fabricated macroscale prototypes and finite element based micromechanical Biomimetic models are employed to measure mechanical response to blunt and penetrating indentation Composite loading. Deformation mechanisms of scale bending, scale rotation, tissue shear, and tissue Natural armor constraint were found to govern the ability of the composite to protect the underlying Fish scale substrate. These deformation mechanisms, the resistance to deformation, and the resulting work of deformation can all be tailored by structural parameters including architectural arrangement (angle of the scales, degree of scale overlap), composition (volume fraction of the scales), morphometry (aspect ratio of the scales), and material properties (tissue modulus and scale modulus). In addition, this network of armor serves to distribute the load of a predatory attack over a large area to mitigate stress concentrations. Mechanical characterization of such layered, segmented structures is fundamental to developing design principles for engineered protective systems and composites. & 2013 Elsevier Ltd. All rights reserved.

1. Introduction et al., 2012; Gemballa and Bartsch, 2002; Ibanez et al., 2009; Jawad and Al-Jufaili, 2007; Sire et al., 2009; Vernerey and Fish scale assemblies provide a diversity of natural engi- Barthelat, 2010). This study focuses on ‘‘elasmoid’’ scale assem- neered designs which achieve multiple functionalities including blies of teleost fish. Individual elasmoid scales are composed of mechanical protection, anisotropic flexibility, hydration, regen- a mineralized outer layer (16–59 vol%) of hydroxyapatite eration, repair, and camouflage (Arciszewski and Cornell, 2006; (Garrano et al., 2012; Torres et al., 2008; Whitear, 1986; Zhu Colbert and Morales, 2001). Examples of design categories of et al., 2012) whose geometry is an ellipsoidal or rectangular fish scale assemblies include structure and composition of the plate with aspect ratios of 25–100. Elasmoid scales are imbri- individual scale (layering), morphometrics or shape of indivi- cated (overlapping), non-articulating and embedded within a dual scales, composite design, inter-scale connections and compliant non-mineralized tissue (Fig. 1), with varying scale joints, and scale assembly spatial arrangements (Garrano aspect ratio, scale orientation angle, spatial overlap, and volume

nCorresponding authors. E-mail addresses: [email protected] (C. Ortiz), [email protected] (M.C. Boyce).

Fig. 1 – Overview of the structure of elasmoid fish scale assemblies. (a) Integument of a fresh Atlantic salmon (Salmo salar) obtained from a local fishery (New Deal Fish Market, Cambridge, MA). Image adapted from O¨ stman, Elisabeth, Iduns kokbok, 1911, Web, Last accessed on May 1, 2012. http://commons.wikimedia.org/wiki/Salmo_salar, (b) overlapping scales and underlying tissue were excised from the main body and caudal peduncle (tail) near the lateral line and (c) micro-computed tomography (lCT) was employed to obtain two-dimensional slices (false coloring) of structure. Scans were performed and analyzed following our previously reported methods (Connors et al., 2012; Song et al., 2010). Scales are embedded in a dermal tissue at various geometric configurations, which are summarized (d). fraction of scales, creating a robust composite system in which where digital image correlation (DIC) was used to measure the interplay between the mineralized scales and the compliant the strain fields in the composite material. These experimental tissue plays a governing role in tailoring and controlling and numerical models yield detailed insights into the roles and mechanical behavior and deformation mechanisms. This com- the tradeoffs of the composite structure providing constraint, posite structure varies not only across species, but also along shear, and bending mechanisms to impart protection and the body of individual fish as found by histological sections flexibility. (Hawkes, 1974; Park and Lee, 1988; Sire, 1990; United States Fish and Wildlife Service, 2010; Whitear, 1986). Experimental measurements of mechanical properties of elasmoid scales have been limited to the macroscale 2. Materials and methods mechanics of an individual scale resisting penetration by a sharp indenter or uniaxial tensile testing. Testing of scales in 2.1. Geometry of elasmoid fish scale assembly a hydrated state found the tensile strength to range between 22 and 65 MPa and the toughness to be 1 MPa (Garrano The primary features of the structure of mineralized scales et al., 2012; Ikoma et al., 2003; Meyers et al., 2012; Torres et al., embedded in a soft tissue are captured in a micromechanical 2008; Zhu et al., 2012). The multilayered elasmoid fish scale model consisting of (1) an upper layer of relatively high was found to localize penetration by promoting cross-like modulus (Es) scale of aspect ratio Ls=ts oriented at angle y fracture patterns in the outer layer (Zhu et al., 2012). On a and embedded in a low modulus (Et) tissue, and (2) a soft (low larger length scale, Vernerey and Barthelat (2010) introduced modulus Et) tissue substrate support (representing the under- a two-dimensional mathematical model of overlapping fish lying collagenous layer) as shown in Fig. 1(c,d). scales where accommodation of bending is determined as a Typical values for the scale thickness in teleost fish are on function of scale geometry and material properties. They the order of ts0:1 mm, but reported values range from found that a strain-stiffening behavior of the assembly with 44 mmto1mm,(Whitenack et al., 2010; Meyers et al., 2012). increasing scale overlap provides the ability to distribute Typical scale lengths, Ls, range from 5 to 15 mm, but have deformation over a large area during bending. been reported over 100 mm long (Francis, 1990; Garrano et al., In this paper, a three-dimensional elastic, composite model 2012; Jawad and Al-Jufaili, 2007; Meyers et al., 2012; Torres was formulated for the case of the mineralized scales fully et al., 2008; Zhu et al., 2012). Despite the large range of embedded in a compliant hyperelastic organic tissue matrix. observed scale lengths and thicknesses, the geometry of the

Loading under the physiologically relevant conditions of fish scale preserves an aspect ratio Ra ¼ Ls=ts between 25 and blunt trauma and indentation is simulated as a function of 100 based on the available literature and measurements. The scale material properties, aspect ratio, scale orientation effect of various geometric parameters will be studied (as angle, spatial overlap, and volume fraction of scales. The discussed later) but the scale will be held at constant aspect simulations allow for identification of deformation mechan- ratio of either Ra ¼50 or 100, which were taken as intermedi- isms, including the roles of scale bending, tissue shear, and ate and maximum values, respectively. scale rotation as a function of scale geometry, and the The scales are initially oriented at angle y relative to a quantification of back-deflection, work of deformation, and compliant tissue support (Fig. 1d). Scales overlap each other spatially heterogeneous stress fields. Macroscale synthetic such that a fraction of the scale is embedded beneath an models were constructed from an engineering thermoplastic adjacent scale. The length d is the exposed length of scale, and silicone rubber using a combination of three-dimensional while the remaining length (Lsd) is embedded beneath printing and molding fabrication methods. The synthetic mod- another scale. This degree of imbrication, or overlap, els were experimentally tested to measure the mechanical Kd ¼ d=Ls is a measure for the spatial overlap defined by performance and to validate the model predictions. Mechanical Burdak (1979), who measured Kd for 16 species of the behavior under blunt compressive loading was measured Cyprinidae family of fish and found that values range from journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 77

0:24rKdr1 depending on species and body location. Fish 1 with highly overlapping, heavily armored skins such as the 40 tench (Tinca tinca), have Kd0, whereas lightly scaled fish have biological range Kd 1, as is the case for undulating eel-like fish. The average 30 number of scales in a cross section of the tissue is normalized 0.5 by the number of scales in a section for the case of zero scale 20 (b) overlap. As this non-overlapping configuration has a Kd of unity (no overlap corresponds to one scale per section), the 10 1 variable Kd is effectively the average number of scales in a (c) (d) cross section. The overlap along the circumference was 0 0 determined to be constant for all species studied by Burdak 00.51

(1979). In most teleost fish species, the upper epidermis K d (scale overlap) follows the contours of the scale pockets (Whitear, 1986), and hence, the irregularity of the surface topology increases as a function of Kd and y. A variable of scale volume fraction, f, can be calculated in terms of the thickness of the dermis between scales td, and scale thickness ts,asf ¼ ts=ðts þ tdÞ. This fraction f represents the scale-to-tissue ratio in the upper, scaled layer and does not include the tissue support, as this bottom layer serves only to capture physiologically relevant deformations in the underlying integument. This bottom tissue layer is fixed at height Htissue ¼ Ls=2. Here, the scale volume fraction is reported as fðKd,y,RaÞ as shown in Fig. 2(a), whereas previous models, neglecting a composite 2 1 system, only consider alinear fraction fKd . This study will 2 vary geometric parameters as governed by the following 1 3 1 25 mm 3 10 mm 10 mm relationship: tan2 y þ 1 Fig. 2 – (a) Map of scale volume fraction / and selected f ¼ KdRa tan y geometries for Ra ¼50. Macroscale 3-D printed and molded synthetic fish scale inspired assembly of ABS (yellow) and An approximate biologically relevant range of fðKd,y,RaÞ is silicone rubber (translucent) and images from digital image shown in Fig. 2(a) based on the available histological sections correlation (DIC) camera prior to loading (center) and and mCT scans (Guinan, 2012; Hawkes, 1974; Park and Lee, deformed (right) for geometries: (b) K ¼0.3, h ¼ 201, /¼0.21, 1988; Sire, 1990; United States Fish and Wildlife Service, 2010; d (c) K ¼0.3, h ¼ 51, /¼0.77 and (d) K ¼0.9, h ¼ 51, /¼0.26. Whitear, 1986). This non-dimensional formulation allows for d d Selected configurations have similar scale overlap (b, c), length-independent analysis of composite assemblies across angle (c, d), and volume fraction (b, d) to demonstrate the a range of length scales. A table of all parameters used in functional effect of each structural parameter. (For study can be found in supplemental Table S1. interpretation of the references to color in this figure caption, the reader is referred to the web version of this 2.2. Prototype fabrication and mechanical testing article.)

Macroscale synthetic prototypes were fabricated and tested to characterize a row of scales in an assortment of geometric geometry Ls ¼50 mm, ts ¼1 mm, were 100 40 50 mm in architectures. A computer aided drawing package (Solid- size, and contained 2–6 repeating scale units depending on

Works, Dassault Syste´mes) was used to create models of angle y and overlap Kd. Material properties of the silicone the scales in a variety of geometric conﬁgurations (Fig. 2). rubber and ABS were measured using compressive and

Scale aspect ratio was kept constant at Ra ¼50 and scale tensile testing, respectively, and found the ABS to silicone fraction f was varied from 0 to 1 by parametrically varying rubber modulus ratio to be 2000. These properties of elastic overlap Kd (0.1, 0.3, 0.5, 0.7, 0.9) and scale angle y (2.51,51,101, modulus (Table 2) are in the range of biological materials for 201,401) for a total of 21 arrangements (Table 1). wet elasmoid scales (Garrano et al., 2012; Lin et al., 2011; These models were exported as stereolithography (.STL) Torres et al., 2008) and ﬁsh tissue (Hebrank and Hebrank, ﬁles for three-dimensional printing using fused deposition 1986). modeling (Dimension BST 1200es, Stratasys). Parts were built Plane strain compression testing of the synthetic proto- with thermopolymer acrylonitrile butadiene styrene (ABS) types was performed (Zwick Z2.5 kN, Zwick/Roel) at a loading with a layer thickness of 0.010 inches and a breakaway rate of 0.1 mm/s to a maximum force of 400 N, corresponding support. The resulting parts were placed in an acrylic frame to approximately 1.5–8.5 mm (equivalently 1.5–8.5 ts) of com- and used as a mold for a translucent silicone rubber (Mold pression depending on geometry. This macroscopic engineer-

Max 10 T, Smooth-On). After the rubber cured, the ABS scales ing stress s ¼ F2=A is calculated from the measured vertical were permanently embedded in the silicone and the frame reaction force, F2, and the initial total sample cross-sectional was removed. The ﬁnal macroscale models had scale (surface) area, A. To provide plane strain conditions for ﬁnite 78 journal of the mechanical behavior of biomedical materials 19 (2013) 75–86

Table 1 – Volume fractions / for geometries studied Ls where Ra ¼50.

f Overlap Kd

Ls 0.1 0.3 0.5 0.7 0.9 2 periodic Angle y 2.51 – – 0.92 0.66 0.51 periodic 1 H 51 – 0.77 0.46 0.33 0.26 3 tissue 101 – 0.39 0.23 0.17 0.13 201 0.62 0.21 0.12 0.09 0.07 401 0.41 0.14 0.08 0.06 0.05 s

Table 2 – Material parameters experimentally determined from synthetic prototype and employed in simulations. H 3 tissue tissue tissue Property Scale Tissue Fig. 3 – Deformation mechanisms under blunt loading with Material 3-D printed ABS Silicone rubber periodic boundary conditions. (a) Undeformed conﬁguration Behavior Elastic Neo-Hookean and boundary conditions for Kd¼0.5, h ¼ 5 deg, /¼0.46 and Modulus E ¼880 MPa E ¼0.39 MPa s 0,t (b) deformed conﬁguration exhibiting local scale curvature n ¼ n : Poisson’s ratio s 0.4 t 0 49 0 jðsÞ, rotation dh ¼ h h, shear strain E12 in tissue, and back

deflection dtissue. thickness geometry, a frame was constructed with thick clear acrylic (PMMA) sheets, constraining the sample in the plate. Simulations which consider the same finite length 3-direction, which was precisely adjusted to account for geometries and the same loading conditions as the experi- slightly varying sample thicknesses. Chalk powder and Teflon mental samples, were conducted and allow for direct compar- sheets were used to reduce friction on the sides and top/ ison of model with experimental results. To simulate bottom of the rubber, respectively. A speckle pattern was structures with many scales, such as those found on the entire applied on the samples with an airbrush and India ink for use length of a fish, periodic boundary conditions were also with optical extensometry via digital image correlation (DIC). imposed on the lateral edges of the scale assembly while Images of the testing were taken at a rate of 1 fps (VicSnap, allowing overall expansion in the 1-direction (Fig. 3a). Further Correlated Solutions) and DIC (Vic-2D 2009, Correlated Solu- simulations were carried out changing the aspect ratio of the tions) was used to track global deformation and obtain local scales, Ra ¼ Ls=ts, from 50 to 100 by increasing the length of the contours of logarithmic (Hencky) strain. Engineering strain scales Ls while holding scale volume fraction f and angle y

E is calculated as the total vertical displacement from DIC, d, fixed. This results in overlap Kd half of that shown in Table 1. normalized by the initial total height, Htotal. Shear strain is Macroscopic engineering stress and strain were calculated reported as engineering shear strain. Data from the digital in the same manner as done experimentally (stress s ¼ F2=A extensometer were then synchronized to mechanical testing and strain E ¼ d=Htotal). Local true Cauchy stress and logarithmic data to obtain engineering stress–strain curves. Back deflec- Hencky strain contours were evaluated at different load levels tion dtissue is defined as deflection in the underlying tissue and to identify the deformation mechanisms which accommo- corresponds to the change in height of the tissue layer Htissue, date the loading for the different composite geometries. as shown in Fig. 3. Back deflections are reported at depth ts For compressive loading, an effective secant stiffness below the scales. 9 ¼ E s ¼ 0:05 MPa s=E was determined and normalized by tissue elastic modulus Et, highlighting the stiffness amplification 2.3. Finite element micromechanical model effect of the scales. Angular rotation dy of individual scales in response to loading was calculated with respect to initial A two-dimensional plane strain composite scale-tissue angle: dy ¼ y0y (Fig. 3). For small bending within an indivi- micromechanical model was simulated using finite element dual scale, the local deformed curvature is described by analysis (FEA). The composite structure was discretized and k ¼ @2y0=@x02 in a rotated coordinate frame (10,20) aligned with modeled with quadratic continuum elements in ABAQUS/ original scale angle y. The average bending curvatureR along a Ls Standard (library types CPE6H and CPE8RH) and a fine mesh scale of deformed length s is given by k ¼ 1=Ls 0 k ds and with elements of length ts=4 was needed to capture the found by extracting the displacements u1 and u2 of nodes deformation within the scales. Tissue and scale elements are along the scale in the mesh. modeled as perfectly bonded with properties found in Table 2. Predatory attack via tooth indentation was simulated with

Non-linear, large deformation theory with frictionless contact rigid indenters of varying radii (R=ts ¼ 0:1,1,10) and a ﬁxed between either a rigid plate or an indenter and the composite half cone angle (y=2) of 301. Such ﬁnite radius indentation was assumed. simulations are more representative of typical scale-tooth A blunt loading event was conducted in the form of a interactions. For these simulations, the thin epidermal tissue distributed compression of the scale assembly with a rigid directly beneath the indenter was removed to account for the journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 79

highly localized aspects of deformation and to increase substantial dependence of back deflection and stiffness on computational efficiency, as this thin outer layer of tissue geometric arrangement of the assembly. Macroscopic loading would be pierced in a physiological setting. In addition, these curves for the finite-sized geometries are shown in Fig. 4(a) indentations were performed on a very large sample (length for three selected geometries (all with scale aspect ratio bLs cos y) to neglect edge effects. For indentation, force is Ra ¼50): (i) Kd ¼0.3, y ¼ 201, corresponding to f¼0.21, (ii) reported F2 per unit width (plane strain) and indentation Kd ¼0.3, y ¼ 51, f¼0.77, and (iii) Kd ¼0.9, y ¼ 51, f¼0.26. These depth is normalized by sample height, d=Htotal. A normalized particular geometries are highlighted because they demon- indentation force per depth (stiffness) is given by F2H=dtissue strate the functional effect of each structural parameter and evaluated at F ¼ F2 ¼ 5 N/mm. individually by sharing similar scale overlap Kd (i, ii), scale angle y (ii, iii), or scale volume fraction f (i, iii). The experimental and simulated loading curves for the same finite 3. Results and discussion length geometries show that all structures studied have an initial non-linear response due to contact conditions from the 3.1. Mechanical protection of finite-sized fish scale irregular loading surface. It was also observed that the bilayer assembly under blunt loading structure of the finite-sized composite allowed the bottom tissue layer of the samples to laterally expand significantly The geometric arrangement of the scale and tissue structure relative to the constrained expansion of the upper scale- governs the response to blunt loading, resulting in a tissue layer (seen in Fig. 5). This result is expected given the

Fig. 4 – Effect of blunt loading on ABS and silicone rubber prototypes under plane strain compression for three selected geometries with Ra¼50. (a) Corresponding experimental and simulation compression stress–strain curves, and back deﬂection as a function of (b) strain and (c) macroscopic stress. Error bars represent standard deviation of n¼3 experiments and solid lines represent simulations of ﬁnite-sized geometry. (d–f) Selected experimental contours of displacement and strain are shown at macroscopic stress r ¼ 0:05 MPa and indicate deformation within the composite structures. 80 journal of the mechanical behavior of biomedical materials 19 (2013) 75–86

additional stiffness of the composite layer (provided by the deform minimally as they rotate relative to the tissue; scales) constrains the lateral expansion of the tissue which deformation is accommodated through tissue shearing. This leads to the barreling-like behavior observed in the bottom effect was largely observed for structures with y4201. Experi- tissue layer, since the tissue near the interface with the upper mental results capture this effect well with the exception of scale-scale layer is constrained and that further away geometries with f1, in which the imaging pattern could not expands. For an infinitely periodic structure, the rubber resolve the very narrow tissue layer between scales (Fig. 4e). cannot expand and is more fully constrained. This edge Scale bending. Upon blunt loading, it can be seen in Fig. 4(f) effect has a strong influence on several aspects of the results that the scales in the arrangement with Kd¼0.9, y ¼ 51 have of the simulations, as discussed later in Section 3.2.1 where noticeably deformed from their original configuration (Fig. 2). the influence of finite-sized specimens is compared to infi- Here, the scales locally bend to accommodate the loading, nitely long periodic structures. resulting in highly localized shear strain in the regions of scale When evaluated at a fixed macroscopic strain, the effect of overlap. Such low overlap results in undesirable localized scale geometry on the maximum back deflection in the under- regions of strain in the tissue substrate, shown in the contours lying tissue was found to be modest. As shown in Fig. 4b, of E22 and E12. Due to the small feature size and non-linear increasing Kd from 0.9 to 0.3 (a 3 increase in f)offereda deformation of the scales during bending, digital image correla- o10% decrease in back deflection dtissue at any fixed strain. tion was not able to fully capture the motion of the scales. It

However, the effective stiffness of the composites is strongly can also be seen for other architectures with Kd40:5 that the dependent on the scale arrangement, and hence, at a fixed scales with low overlap underwent significant local bending, macroscopic stress, the same 3 increase in f offers a 30–40% often constrained by three or more points of inflection. decrease in back deflection (Fig. 4c). Given that predatory Tissue constraint. The scale layers imposed a significant attacks are often force-limited, these results show how geo- constraint on the underlying tissue, constraining lateral metric scale configurations and compositions observed in expansion. This constraint is apparent in the deformed nature can protect underlying tissue by limiting tissue straining images of Fig. 5, which shows the constrained bulging of as expected. By tailoring the structural parameters, species are the underlying tissue in the finite strained samples. This able to control the local protective function of their armors. constraint effect will be shown to provide significant stiffen- Experimental contours of displacement and strain agree well ing and hence dramatic reduction in back deflection of the (Figs. 4 and 5) with simulated results of the same geometry, overall composites when evaluating the periodic structure. demonstrating the quantitative capabilities of the model and Loading curves from experiments on physical prototypes providing insights into the deformation mechanisms. Depend- agree well (Fig. 4a) with simulations of the same geometry ing on the geometric arrangements and volume fractions of the and display the behavior of the composite structure. A secant scales, macroscopic loading is accommodated by either (1) stiffness was extracted from loading curves at a fixed macro- global tissue shear between scales and scale rotation, (2) local scopic stress of s¼0.05 MPa (corresponding to E ¼ 0:020:17) tissue shear at scale tips and scale bending, or (3) constraint of and was found to range from E ¼ 1–3 across the geometries the tissue and overall stiffening. These deformation mechan- studied (Fig. 6a). This secant stiffness captures the effective isms are illustrated using the three selected geometries in ‘‘springs in series’’-like stiffness of the tissue support layer Figs. 4 and 5. and the scaled layer. Assemblies with a low volume fraction

Tissue shear and scale rotation. As shown in the contours of of scales had EEt; indirectly, these low volume fraction scale

Fig. 4(d) for Kd ¼0.3, y ¼ 201, the anisotropy from the angled assemblies do not limit back deflection. Increasing f from 0 scales couples the compressive loading to a shear strain E12 to 0.25 promotes a nearly linear increase in E from 1 to 2 and within the tissue. For similar architectures with high scale further increasing f gives a plateau of E ¼ 3atf ¼ 0:5. These overlap (low Kd) and initial angle y, this region of shear strain results show the effect of increasing f on limiting back is broad and evenly distributed over the length of the scales. deflection and suggest a plateau of influence at f ¼ 0:5. While This mechanism of shear between scales promotes uniform effective stiffness of the composite is one indicator of the scale rotation, as shown in Figs. 4(d) and 5(a). Here, the scales protective response of the system, it does not explicitly

Fig. 5 – Simulated contours of displacement and strain are shown at macroscopic stress r ¼ 0:05 MPa corresponding to experiments of blunt loading of physical models in Fig. 4. The bottom tissue layer is shown to laterally bulge relative to the upper scale-tissue layer. Similar results were observed experimentally (not shown). (a) Kd ¼0.3, h ¼ 20 deg, corresponding to

/¼0.21, (b) Kd ¼0.3, h ¼ 5 deg, /¼0.77 and (c) Kd ¼0.9, h ¼ 5 deg, /¼0.26. journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 81

describe the effects experienced in the underlying tissue. To on tissue deformation for geometries with stiff upper scale- function as an effective dermal armor, fish scales must tissue layers, in which the expansion of the lower layer is minimize the deflections, strains and/or stresses beneath constrained by the presence of and compatibility with the the scale layer to protect the body. Experimental results show scale layer. To eliminate these boundary effects, a periodic that back deflection in the underlying tissue, dtissue, decreases structure was simulated to more accurately model a larger as scale volume fraction increases for fo0:5 and then number of repeating scales along the length, such as those remains at dtissue=Ltissue 0.04 for f40:5(Fig. 6b). found along the length of a fish body. The resulting loading curves and contours for the periodic structure are shown in Fig. 7, which demonstrate the large 3.2. Mechanical protection of infinitely long (periodic) fish difference the constraint from periodicity has on the results scale assembly under blunt loading for geometries with high f. Imposing periodic boundary conditions has little effect for small volume fraction 3.2.1. Deformation mechanisms in periodic structures (fo0:2), but as f increases, the effective stiffness of the Since the actual structures consist of many repeating scales periodic scale structure increases by an order of magnitude along the length of the fish body, simulations with periodic over the finite length structures, which had permitted lateral boundary conditions which capture an infinitely long struc- deformation (bulging) of the underlying tissue. The effective ture provide a more physiologically relevant assessment of stiffness of the periodic structure follows a nearly linear the mechanical response than the simulations of the finite- relationship with scale fraction f (Fig. 9(a)) and shows the sized specimens. Recall the finite-sized specimens exhibited direct effect that increasing scale armor has on limiting back significant lateral expansion (bulging) of the bottom soft deflection at a given macroscopic stress level (Fig. 9(b)). This tissue substrate (Fig. 5) due to the unconstrained lateral relationship between back deflection and scale volume frac- edges. The relaxed boundary conditions in these finite-sized tion demonstrates that the volume fraction of scales governs specimens cause the structures to exhibit a more compliant the constraint of the tissue layer and in turn, has a significant response. In an infinitely periodic structure, the lateral strain influence on protection. Therefore, effective stiffness and of both layers must be identical based on the compatibility. back deflection can be adjusted by tailoring the scale fraction

The implications of this constraint have a dramatic impact fðKd,yÞ. One aspect of the constraint effect of increased f on effective stiffness is demonstrated in the geometry of Fig. 7(c), which has the same overlap as Fig. 7(b) but a signiﬁcantly higher scale volume fraction, which was achieved by reducing the angle of the scales from 201 to 51, resulting in a stiffer loading curve and far less penetration in

the underlying tissue (u2,dtissue) at a given force. In this case, by reconfiguring the angle of the same number of scales in a 1 cross section (Kd ), the system can achieve a 4 increase in penetration resistance. These results show how the geometric arrangement of the scales and the scale volume fraction, together with their influence on constraining the Fig. 6 – Experimental and finite sized simulation results for deformation of the underlying tissue, serve to provide protec-

21 total geometries with Ra¼50. (a) Stiffness and (b) back tion. Furthermore, such scale-imposed tissue constraint deﬂection in response to blunt loading are evaluated at could serve as a design principle for these composite struc- r ¼ 0:05 MPa. tures to locally tailor stiffness.

Fig. 7 – Periodic simulations for Ra¼50 yield insights into deformation mechanisms of periodic scale assembly under blunt loading. (a) Loading curves demonstrate stiffening constraint for structures with high /. Contours are evaluated at r ¼ 0:05 MPa, (b) large initial scale h promotes rotation of scales via uniform tissue shearing (E12), (c) high scale volume fraction directly results in a stiff composite, which reduces back deﬂection in the underlying tissue u2 and (d) geometries with little scale overlap (high Kd) exhibit excessive scale bending (r11) and localized high stress (r22) and strain in the underlying tissue. 82 journal of the mechanical behavior of biomedical materials 19 (2013) 75–86

The underlying deformation mechanisms for the structures Here for the same volume fraction of scales f and a given with periodic boundary conditions were also identified. Simi- fixed y, the increase of aspect ratio reveals a tradeoff between lar to results from finite-sized geometry, scale bending, scale dominant deformation mechanisms. Increasing the aspect rotation, and tissue shear were found to be the primary ratio via reducing Kd increases the effective stiffness E of the modes of deformation. The mechanisms of scale bending assemblies, resulting in a reduced back deflection in the and rotation are dependent on initial overlap (Kd) and angle underlying tissue (Fig. 9). To examine the mechanics that

(y)(Fig. 9). Architectures with low overlap (high Kd1) are govern this response, scale bending dy and rotation k were dominated by scale bending, while those with high initial evaluated for the infinitely periodic case. Bending within the angle y are dominated by tissue shearing and corresponding scales was reduced for higher aspect ratio simulations, which scale rotation. This behavior is demonstrated by the high is explained by the corresponding decrease in scale overlap. values of contours of bending stress (s11) found within the However, the trend in Fig. 9(c) suggests that scale with the minimally overlapping scales in Fig. 7(d) for a macroscopic same overlap Kd and increased aspect ratio would bend much stress of s ¼ 0:05 MPa. Scales in such configurations at this more than those with the original aspect ratio, showing the 1 load have an effective curvature of k40:25Ls , or equiva- large influence of Ra on the local deflections and bending lently, an effective bending radius of Ro4Ls. Conversely, the curvature of the scales. Despite the same fraction of tissue in large initial angle y in Fig. 7(b) results in a shear straining (E12) the composite, shearing of the tissue was notably reduced. of the tissue, which in turn, leads to the rotation of the scales. Hence, while scale bending increased, scale rotation was

Structures with both high Kd and y (corresponding to fo0:1) found to significantly decrease. This is noteworthy because exhibit both significant scale bending and scale rotation, but previous results suggest scale angle y (here, fixed) governs such configurations are typically not observed in nature. tissue shear and scale rotation. This transition from tissue shear plus scale rotation to scale bending with increasing 3.2.2. Work of deformation aspect ratio served to stiffen the composite, yet resulted in To determine the ideal armor architecture under blunt loading, elevated levels of local bending stress within the scales. the deformation resistance of thecompositemustbeevaluated These higher bending stresses will lead to early failure of against competing mechanical functionalities. Given that the the scales via yielding or fracture. stiffness of structures (E) and their work of deformation (W ) Alternatively, the aspect ratio of the scales can be are inversely related when evaluated at a fixed load, it is increased by fixing the scale volume fraction f and the scale problematic to select a structure that combines both high overlap Kd and varying the scale angle y. Changing the fixed stiffness and high work of deformation. Thus, if both proper- parameters results in a completely different structural ties of high E and W are desired, an intermediate value of f arrangement, as shown in Fig. 8(d). This structure with fixed must be selected to balance these two criteria. f,Kd,Ra results in both more bending and rotation than the original structure, yet is less stiff. These results further 3.2.3. Effect of scale morphometry suggest that aspect ratio alone cannot govern the deforma-

Increasing the aspect ratio of scales Ra ¼ Ls=ts from 50 to 100 tion mechanisms of the structure and that the response is a was performed in three ways: (a) ﬁxing f,y and varying Kd, (b) function of composition (f), structural arrangement (Kd,y)

fixing Kd,y and varying f, and (c) fixing f,Kd and varying y. and morphometry (Ra). The resulting geometries, stress–strain curves, and contours In general, the morphometry of the scales helps to govern of s22 are shown in Fig. 8. To compare the same composition the dominant deformation mechanism of the assembly, but and contact geometry of varying architectures, scale volume is dependent on the spatial arrangement of the scales. fraction f and angle y were held constant and evaluated for Typically, thin, high aspect ratio scales result in deformations all geometries as a function of fðKd,y,Ra ¼ 100Þ. This combi- primarily dominated by bending, whereas thick (low aspect nation of parameters is reflected in Fig. 8(b), while Fig. 8(a) ratio) scales are dominated by tissue shear plus scale rota- shows the original structure from the previous discussion. tion. This tradeoff can be tailored by adjusting individual

Fig. 8 – Effect of scale morphometry. Increasing scale aspect ratio Ra ¼ Ls=ts from 50 to 100 as a function of varying Kd; h; /.

Stress–strain curves and contours of r22 are shown for these combinations of geometric parameters. Architecture in (a) is used in Section 3.2.1 and (b) in Section 3.2.3. journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 83

Fig. 9 – Deformation mechanisms for uniform compression evaluated at a macroscopic stress of r¼0.05 MPa for 21 total geometries with Ra¼50 and 100. (a) For low scale volume fractions (/o0:25) in experiments and finite length simulations, effective loading stiffness E of the composite increases linearly with scale fraction then plateaus for /40:5. Similarly, back deflectionintheunderlyingtissue,dtissue, decreases linearly for /o0:5. Periodic simulations suggest that this plateau for large / is a boundary effect. For periodic simulations, (c) microscopic scale bending is primarily a function of overlap Kd,whereas(d)scale rotation is dependent on initial scale h. Transition from rotation to bending is evident for large Ra (dashed line). scale aspect ratios in addition to other properties, e.g. elastic The similarity of both the loading curves and the back modulus, internal structure, and porosity of the scales. deflection corresponding to Kd ¼0.3, y ¼ 201, f¼0.21, and

Kd ¼0.3, y ¼ 51, f¼0.77 indicates that the common overlap of

3.3. Mechanical protection of ﬁsh scale assembly under Kd ¼0.3 controls the mechanical response of the composite. In predatory tooth attack contrast, the response for Kd ¼0.9, y ¼ 51, f ¼ 0:26 is much

more compliant and permits more back deflection dtissue in While blunt loading predicts the behavior of the assembly to the underlying tissue because of the minimally overlapping large indenters (RbKdLs), threats are often localized to a small scales of Kd ¼0.9. Localized indentations of R=ts ¼ 0:1 are area. Idealizing predatory biting as a sharp tooth of radius R, primarily accommodated through the mechanism of scale the corresponding contact area and the resulting bending, which is isolated to only a few scales. Evaluating deformation-induced scale-tissue interactions govern the across all architectures fðKd,yÞ, the overlap of the scales (Kd) number of scales that are involved in the deformation. For governs the ability of the composite to resist penetration physiologically relevant indentation (RoKdLs), the indenter (Fig. 11). Normalized indention force (local stiffness) only comes into direct contact with one scale. Underlapped increases with increasing scale overlap (decreasing Kd). Simi- and adjacent scales are also deformed, as governed by Kd. larly, back deflection in the underlying tissue was found to Under low penetration loads, the scales are not locally decrease with overlap such that architectures with highly indented, but rather undergo significant bending with the overlapping scales (Kd0) are very stiff and had minimal back compliant tissue between the scales shearing and the tissue deflection. Due to the localized, non-uniform deformation of beneath the scales also shearing (Fig. 10). For the case of a the assembly under finite indentation, scale rotation is no conical rigid indenter tip at low loads (F¼5 N/mm), there is a longer a dominant deformation mechanism. In these layered single point of contact and the resulting loading curves and composite structures, the overlap, angle, and volume fraction underlying tissue deformation were found to be nearly work together to give interplay between scale bending and identical for the range of R=ts ¼ 0:1,1,10 simulated. Note that shearing of the tissue to involve more material. These this force of F¼5 N/mm is only relevant for the materials geometries are mechanisms for increasing work of deforma- properties and scale size shown in Table 2 where Ra ¼50 and tion by involving greater amount of material laterally as well

Htissue ¼ Ls=2. as to deeper depths. 84 journal of the mechanical behavior of biomedical materials 19 (2013) 75–86

Fig. 10 – Indentation on ﬁsh scale assembly for radius R=ts ¼ 0:1. (a) Loading curves for three geometries show that indentation force is nearly identical for architectures with similar overlap, despite very different h; / and (b) corresponding underlying back deﬂection and (d–f) contours of stress, strain taken at F¼5 N/mm.

0 0 0.2 0.4

Fig. 11 – Indentation force and back deﬂection evaluated at ¼ F 5 N/mm across all scale assembly architectures s = 0.1

/ðKd; h; Ra ¼ 50Þ for a sharp indenter with radius R=ts ¼ 0:1. s = 10

Overlap Kd governs the ability of the composite to resist penetration, which is dominated by the deformation Fig. 12 – Indentation loading curves for varying indenter mechanism of scale bending. geometry (R=ts ¼ 0:1; 10) show little effect of R on mechanical response due to point-wise interaction for small loading. At larger loads, the scale deforms around the indenter Larger indenters (R4K L and simulated for R=t ¼ 10 as d s s radius and the reaction force increases. Contours shown of shown in Fig. 12) under large penetration loads permit the scale r for geometry with K ¼ 0:3; h ¼ 5 deg; / ¼ 0:77. to bend around the indenter. Above F¼10 N/mm, these larger d radius indenters produce a stiffer behavior as the contact area between scale and tooth increases. For indenters whose radii span multiple scales, the load is distributed across the scale assembly which reduces deflections, scale deformation, and stress distributions within the scales and tissue give insight to stress concentrations, thereby protecting the fish. This explains failure modes and locations resulting from excessive deforma- why predators benefit from having sharper teeth: by localizing tion. High shear strain E12 of the tissue promotes failure by the biting force to a small contact area, the local contact stresses delamination of the tissue-scale interface, which permits scales are increased. This effect is compounded for segmented systems to dislodge and damage the structure of the composite. Alter- such as fish scales, whereby if one scale sees too much bending, natively, regions of high bending stress s11 of the scale promote the scale and subsequently the entire assembly can be defeated. yield and fracture of the scale. Sharper radius teeth permit predators with a given biting force to isolate a single scale and penetrate the underlying tissue. By localizing the indentation deformation to a finite region, pre- 4. Conclusions dators with a given biting force are able to penetrate the underlying tissue. While this elastic model does not incorporate failure Fish scale armor provides a model biomimetic composite for mechanisms such as fracture, delamination, or plasticity, the the design of structures to provide global penetration journal of the mechanical behavior of biomedical materials 19 (2013) 75–86 85

resistance and ﬂexibility. Biological systems have a limited contract W911NF-07-D-0004 and Institute for Collaborative library of materials available, often consisting of rigid miner- Biotechnologies (ICB) under contract DAAD-19-02-D0002. alized components and compliant organic tissues. The morphology and architecture of the material organization is one unique way to provide a spectrum of structural functional- Appendix A. Supplementary data ities. Overlapping scale units distribute stresses across a large volume of material and provide penetration resistance at a Supplementary data associated with this article can be found reduced weight (and subsequent cost of mineralization) in the online version at http://dx.doi.org/10.1016/j.jmbbm.2012. compared to a continuous armor layer. Scale architecture 11.003.

(Kd, y), composition (f), and morphometry (Ra) can be used to locally tailor composite stiffness and back deflection in the references underlying tissue in order to achieve protection. The flexibility of the scales and tissue permits the scales to rotate and bend under applied loading. Assemblies of these scaled Arciszewski, T., Cornell, J., 2006. Bio-inspiration: learning creative structures are formed without joints or hinges, forming a design principia. In: Smith, I. (Ed.), Intelligent Computing in simple, easily adaptable design. The degree of flexibility or Engineering and Architecture. Springer, Berlin, Germany. pp. 32–53. protection is reconfigurable by simply changing morphome- Burdak, V.D., 1979. Morphologie fonctionnelle du te´gument ećailleux try and the overlap distribution of the scales. des poissons. Kiev: La Penseé Scientifique (in Russian). French Under blunt loading, the composition primarily governs the translation, Cybium 10, 1986, 1–147. effective response of the composite, which is achieved by a Colbert, E.H., Morales, M., 2001. Colbert’s Evolution of the Vertebrates: combination of deformation mechanisms controlled by the A History of the Backboned Animals Through Time. Wiley-Liss. microstructural arrangement. Inclusion of a compliant tissue Connors,M.J.,Ehrlich,H.,Hog,M.,Godeffroy,C.,Araya,S.,Kallai,I., Gazit, D., Boyce, M.C., Ortiz, C., 2012. Three-dimensional struc- is key to understanding the true behavior of the composite, ture of the shell plate assembly of the chiton Tonicella mar- which is dominated by tissue constraint, tissue shearing (and morea and its biomechanical consequences. Journal of resulting scale rotation), and scale bending. Volume fraction Structural Biology 177, 314–328. f governs constraint, effective stiffness, and back deflection; Francis, R., 1990. Back-calculation of fish length: a critical review. scale overlap Kd governs scale bending, and initial scale angle Journal of Fish Biology 36, 883–902. y governs tissue shearing and scale rotation. The influence of Garrano, A.M.C., Rosa, G.L., Zhang, D., Niu, L.N., Tay, F., Majd, H., these mechanisms can be tailored by adjusting the scale Arola, D., 2012. On the mechanical behavior of scales from Cyprinus carpio. Journal of the Mechanical Behavior of Bio- morphometry: for scales with a large aspect ratio, the medical Materials 7, 17–29. deformation mechanisms will be dominated by scale bend- Gemballa, S., Bartsch, P., 2002. Architecture of the integument in ing. Conversely, scales with small aspect ratio will rotate lower teleostomes: functional morphology and evolutionary under blunt loading, accommodated by tissue shearing. implications. Journal of Morphology 253, 290–309. As the contact area of the loading surface is reduced to a Guinan, M.J., Anatomy 100: Integument, University of California at / finite radius penetration indentation, there is a transition Davis Lecture. http://guppiesonli.wordpress.com/guppy-arti S from tissue constraint and scale rotation to a deformation cles/skin-structure-of-guppy/ . Last accessed May 1, 2012. Hatjasalo, L., Rinko, K., 2006. Elastic composite structure. US dominated by localized scale bending, which is accommo- Patent 7153789. dated by shearing of the tissue interlayers and the underlying Hawkes, J., 1974. Structure of fish skin 1: general organization. tissue substrate and governed by the overlap of the scales. Cell and Tissue Research 149, 147–158.

Architectures with high scale overlap (low Kd) resist penetra- Hebrank, M.R., Hebrank, J.H., 1986. The mechanics of fish skin: tion by distributing loading over a large area. Deformation of lack of an external tendon role in two teleosts. The Biological a scale during localized bending could risk failure by plastic Bulletin 171, 236. Ibanez,A.,Cowx,I.,O’Higgins,P., 2009. Variation in elasmoid fish deformation or fracture, exposing the underlying tissue and scale patterns is informative with regard to taxon and swimming defeating the armor. Here, highly overlapping scales are mode. Zoological Journal of the Linnean Society 155, 834–844. beneficial as they provide multiple layers of defense; in order Ikoma, T., Kobayashi, H., Tanaka, J., Walsh, D., Mann, S., 2003. to penetrate the tissue, the indenter must deform and defeat Microstructure, mechanical, and biomimetic properties of fish 1 Kd scales. Alternatively, while scale rotation risks injury to scales from Pagrus major. Journal of Structural Biology 142, the compliant tissue by delaminatation or tearing, the stiff 327–333. scale protective layer remains intact. Such mechanical char- Jawad, L., Al-Jufaili, S., 2007. Scale morphology of greater lizard- fish Saurida tumbil (Bloch, 1795)(Pisces: Synodontidae). Journal acterization could have useful applications in developing of Fish Biology 70, 1185–1212. principles for protective systems (Neal and Bain, 2004), Kim, S., Su, Y., Mihi, A., Lee, S., Liu, Z., Bhandakkar, T.K., Wu, J., composite textiles (Hatjasalo and Rinko, 2006), and even Geddes III, J.B., Johnson, H.T., Zhang, Y., Park, J.K., Braun, P.V., electronics (Kim et al., 2012). Huang, Y., Rogers, J.A., 2012. Imbricate scales as a design construct for microsystem technologies. Small 8, 901–906. Lin, Y.S., Wei, C.T., Olevsky, E.A., Meyers, M.A., 2011. Mechanical properties and the laminate structure of Arapaima gigas scales. Journal of the Mechanical Behavior of Biomedical Acknowledgments Materials 4, 1145–1156. Meyers, M., Lin, Y.S., Olevsky, E.A., Chen, P.Y., 2012. Battle in the This research was supported by the U.S. Army Research Office Amazon: Arapaima vs. Piranha. Advanced Engineering Mate- through the MIT Institute for Soldier Nanotechnologies under rials 14, B279–B288. 86 journal of the mechanical behavior of biomedical materials 19 (2013) 75–86

Neal, M.L., Bain, A.D., 2004. Method and apparatus for defeating and Engineering C: Materials for Biological Applications 28, ballistic projectiles. US Patent 6745661. 1276–1283. Park, E., Lee, S., 1988. Scale growth and squamation chronology for United States Fish and Wildlife Service, 2010. Normal trout histol- the laboratory-reared hermaphroditic fish Rivulus marmoratus ogy. http://training.fws.gov/ec/fish/histo1.html. Last accessed (Cyprinodontidae). Japanese Journal of Ichthyology 34, 476–482. May 1, 2012. Sire, J., 1990. From ganoid to elasmoid scales in the actinopter- Vernerey, F.J., Barthelat, F., 2010. On the mechanics of fishscale ygian fishes. Netherlands Journal of Zoology 40, 75–92. structures. International Journal of Solids and Structures 47, Sire, J.Y., Donoghue, P.C.J., Vickaryous, M.K., 2009. Origin and 2268–2275. evolution of the integumentary skeleton in non-tetrapod Whitear, M., 1986. The skin of fishes including cyclostomes: epider- vertebrates. Journal of Anatomy 214, 409–440. mis.In:Bereiter-Hahn,J.,Matoltsy,A.,Richards,K.(Eds.),Biology Song, J., Reichert, S., Kallai, I., Gazit, D., Wund, M., Boyce, M.C., oftheIntegument.Springer,Berlin,Germany.pp.8–38. Ortiz, C., 2010. Quantitative microstructural studies of the Whitenack, L.B., Simkins Jr., D.C., Motta, P.J., 2010. Biology meets armor of the marine threespine stickleback (Gasterosteus engineering: the structural mechanics of fossil and extant aculeatus). Journal of Structural Biology 171, 318–331. shark teeth. Journal of Morphology 272, 169–179. Torres, F.G., Troncoso, O.P., Nakamatsu, J., Grande, C.J., Gomez, C.M., Zhu,D.,Ortega,C.F.,Motamedi,R.,Szewciw,L.,Vernerey,F.,Barthelat, 2008. Characterization of the nanocomposite laminate structure F., 2012. Structure and mechanical performance of a modern fish occurring in fish scales from Arapaima gigas. Materials Science scale. Advanced Engineering Materials 14, B185–B194.